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arXiv · 1611.03118

Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs

Christian Reiher·Vojtěch Rödl·Andrzej Ruciński·Mathias Schacht·Endre Szemerédi
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Abstract

We show that every 3-uniform hypergraph with $n$ vertices and minimum vertex degree at least $(5/9+o(1))\binom{n}2$ contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal.

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Christian Reiher, Vojtěch Rödl, Andrzej Ruciński, Mathias Schacht, Endre Szemerédi. 2019-01-28. Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs. https://doi.org/10.1112/plms.12235

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